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Rama09 [41]
3 years ago
15

Three components are randomly sampled, one at a time, from a large lot. As each component is selected, it is tested. If it passe

s the test, a success (S) occurs; if it fails the test, a failure (F) occurs. Assume that 79% of the components in the lot will succeed in passing the test. Let X represent the number of successes among the three sampled components.
Find P(SFS) and P(SSF)
Mathematics
1 answer:
satela [25.4K]3 years ago
7 0

Answer:

The probability of SFS and SSF are same, i.e. P (SFS) = P (SSF) = 0.1311.

Step-by-step explanation:

The probability of a component passing the test is, P (S) = 0.79.

The probability that a component fails the test is, P (F) = 1 - 0.79 = 0.21.

Three components are sampled.

Compute the probability of the test result as SFS as follows:

P (SFS) = P (S) × P (F) × P (S)

            =0.79\times0.21\times0.79\\=0.131061\\\approx0.1311

Compute the probability of the test result as SSF as follows:

P (SSF) = P (S) × P (S) × P (F)

            =0.79\times0.79\times0.21\\=0.131061\\\approx0.1311

Thus, the probability of SFS and SSF are same, i.e. P (SFS) = P (SSF) = 0.1311.

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